National Center for Teacher Effectiveness

Mathematical Quality of Instruction (MQI)

The MQI is a Common Core-aligned observational rubric that provides a framework for analyzing mathematics instruction in several domains. Within each of the five domains, individual codes contain score points that categorize instruction into different levels of quality. The MQI was developed in order to provide a both multidimensional and balanced view of mathematics instruction.

NCTE Tools

One of the goals of NCTE is to provide valid and reliable tools to the field of education. The links below will connect you to the instruments that NCTE developed and/or used in the core study. Additionally, NCTE developed a Video Library that contains video examples of a range classroom mathematics instruction in the United States, and project data from the core study is archived at the Interuniversity Consortium for Political and Social Research (ICPSR).  

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Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices that support student achievement. Economics of Education Review , 48, 16-29. Publisher's VersionAbstract

Recent investigations into the education production function have moved beyond traditional teacher inputs, such as education, certification, and salary, focusing instead on observational measures of teaching practice. However, challenges to identification mean that this work has yet to coalesce around specific instructional dimensions that increase student achievement. I build on this discussion by exploiting within-school, between-grade, and cross-cohort variation in scores from two observation instruments; further, I condition on a uniquely rich set of teacher characteristics, practices, and skills. Findings indicate that inquiry-oriented instruction positively predicts student achievement. Content errors and imprecisions are negatively related, though these estimates are sensitive to the set of covariates included in the model. Two other dimensions of instruction, classroom emotional support and classroom organization, are not related to this outcome. Findings can inform recruitment and development efforts aimed at improving the quality of the teacher workforce. 

NCTE Student Assessments

Developed jointly by Harvard and Educational Testing Services (ETS), the NCTE Student Assessment is an open resource for use by researchers and practitioners (not commercial ventures). The assessment was designed to be sensitive to teachers' mathematical knowledge for teaching and instruction, and to measure gains resulting from teacher professional development. Additionally, the NCTE Student Assessments are aligned to the 4th and 5th grade Common Core Standards in Mathematics.

The items on the NCTE assessment have a unique "nested set" design which assesses the understanding...

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John Papay

John Papay

Affiliated Researcher; SDP Fellowship Faculty Advisor
Assistant Professor of Education and Economics
Department of Education, Brown University
Kelcey, B., Hill, H. C., & McGinn, D. (2014). Approximate measurement invariance in cross-classified rater-mediated assessments. Frontiers in Psychology , 5 (1469). Publisher's VersionAbstract

An important assumption underlying meaningful comparisons of scores in rater-mediated assessments is that measurement is commensurate across raters. When raters differentially apply the standards established by an instrument, scores from different raters are on fundamentally different scales and no longer preserve a common meaning and basis for comparison. In this study, we developed a method to accommodate measurement noninvariance across raters when measurements are cross-classified within two distinct hierarchical units. We conceptualized random item effects cross-classified graded response models and used random discrimination and threshold effects to test, calibrate, and account for measurement noninvariance among raters. By leveraging empirical estimates of rater-specific deviations in the discrimination and threshold parameters, the proposed method allows us to identify noninvariant items and empirically estimate and directly adjust for this noninvariance within a cross-classified framework. Within the context of teaching evaluations, the results of a case study suggested substantial noninvariance across raters and that establishing an approximately invariant scale through random item effects improves model fit and predictive validity.

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